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020 _a9783319107776
_9978-3-319-10777-6
024 7 _a10.1007/978-3-319-10777-6
_2doi
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_2bicssc
072 7 _aMAT007000
_2bisacsh
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_2thema
082 0 4 _a515.352
_223
100 1 _aLiebscher, Stefan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aBifurcation without Parameters
_h[electronic resource] /
_cby Stefan Liebscher.
250 _a1st ed. 2015.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXII, 142 p. 34 illus., 29 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2117
505 0 _aIntroduction -- Methods & Concepts -- Cosymmetries -- Codimension One -- Transcritical Bifurcation -- Poincar ́e-Andronov-Hopf Bifurcation -- Application: Decoupling in Networks -- Application: Oscillatory Profiles -- Codimension Two -- egenerate Transcritical Bifurcation -- egenerate Andronov-Hopf Bifurcation -- Bogdanov-Takens Bifurcation -- Zero-Hopf Bifurcation -- Double-Hopf Bifurcation -- Application: Cosmological Models -- Application: Planar Fluid Flow -- Beyond Codimension Two -- Codimension-One Manifolds of Equilibria -- Summary & Outlook.
520 _aTargeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
650 0 _aDifferential equations.
650 0 _aPartial differential equations.
650 0 _aDynamics.
650 0 _aErgodic theory.
650 1 4 _aOrdinary Differential Equations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12147
650 2 4 _aPartial Differential Equations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12155
650 2 4 _aDynamical Systems and Ergodic Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319107783
776 0 8 _iPrinted edition:
_z9783319107769
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2117
856 4 0 _uhttps://doi.org/10.1007/978-3-319-10777-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
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